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I am trying to understand CUSUM or Cumulative Sum Control Chart.

In the example on above linked Wikipedia page, the formula for high CUSUM value indicating positive anomaly is given as:

$$S_{H_{n+1}}=\max(0, S_{H_n}+Z_n-\omega)$$

Similarly, formula for low CUSUM value, indicating negative anomaly is given by:

$$S_{L_{n+1}}=\max(0, S_{L_n}-Z_n-\omega)$$

However, I am not able to understand what is to be taken as the value of $\omega$ or omega in these formulae?

User1865345
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rnso
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  • It's a tunable parameter. Its value is adjusted to achieve an acceptable balance of the average run length of below-threshold values (when the process is out of control), which you want to be very long, against the expected time to observe an above-threshold value when the process is out of control, which you want to be very short. – whuber Jun 29 '23 at 19:24

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